Functions of several variables

A more intricate example of broadcasting arises when building functions of several variables. Suppose, for instance, that we were given two functions of one variable, and , and that we want to construct a new function, , according to the formula:

 This is clearly a valid mathematical definition. We would like to express this definition as the sum of two functions in two variables defined as

,

and now we may simply write:

The situation is similar to that arising when adding a column matrix and a row matrix:

C = arange(2).reshape(-1,1) # column
R = arange(2).reshape(1,-1) # row
C + R                       # valid addition: array([[0.,1.],[1.,2.]])

This is especially useful when sampling functions of two variables, as shown in Section 5.5.3: Typical examples.